After Sam Tully had struck the upright from a Ballinteer counter-attack, Quinn was in the right place at the right time to slot home from close range and get St John's over the line against a home side that finished with 12 men following three second-half dismissals.
The visitors were the sharper outfit from the opening whistle with the impressive Donal Gormley kicking a fine score early on to add to frees by Fearghal Duffy and Glenn Whelan.
Plunkett's, in contrast, were struggling to find their rhythm but were given a much needed boost when Jamie Bray finally opened their account with a well-taken goal at the end of the first quarter.
St John's remained in the ascendancy, however, with centre-back Stephen Fitzsimons and wing-back Conor McDaid influential and a brace of Whelan frees ensured them a narrow interval lead.
With Duffy having pulled up with a hamstring injury, St John's lost some of their attacking threat and despite their numerical disadvantage, Plunkett's responded well.
Dublin minor Niall Walsh landed two frees to keep the contest on a knife edge with Ballinteer largely dependent on placed balls to preserve their narrow lead.
Shane Darcy and Bray pointed for the hosts, but their efforts proved in vain as St John's finally made the most of the increased space to settle the tie through Quinn's vital contribution.
Holders Thomas Davis will face Ballinteer in the final following their 2-6 to 0-11 comeback victory over Raheny at Kiltipper Road last night.
The visitors started brightly with Gavin Ivory impressing at centre-forward but their half-time lead was eroded by the 43rd minute thanks to two goals within four minutes from Dean Brennan while late points from the impressive Adam Fallon and Paul Hudson completed the turnaround.